Matthew's Asgn

I decided that I would attempt to perform a simple analysis of a series RL circuit, which could then be used to do a more complex analysis on a basic transformer. I have always had interest in electronics, and transformers are key to basic electronics.

I decided that i would do the analysis of a RL circuit with the variables instead of given values.

Given:

V(t)=$\cos w*t\,\!$

V(s)=$\ s/(s^{2}+w^{2})\,\!$

I(0)=i

The Laplace transform for an inductor:

$\displaystyle {\mathcal {L}}\left\{f(t)\right\}$ = $\ Ls+Li\,\!$

The Laplace transform for a resistor:

$\displaystyle {\mathcal {L}}\left\{f(t)\right\}$ = $\ R\,\!$

Therefore the Resulting Equation for the system after applying the Laplace Transform:

$\ 0=-s/(s^{2}+w^{2})+RI(s)+LsI(s)-Li\,\!$

A series of algebraic manipulations follows to come up with I(s):

$\ s/(s^{2}+w^{2})=(R+Ls)I(s)+Li\,\!$

$\ I(s)=s/((s^{2}+w^{2})(R+Ls))-Li/(R+Ls)\,\!$